Phase transfer of highly monodisperse iron oxide nanocrystals with Pluronic F127 for biomedical applications

Iron oxide nanoparticles made from the thermal decomposition method are highly uniform in all respects (size, shape, composition and crystallography), making them ideal candidates for many bioapplications. The surfactant coating on the as-synthesized nanoparticles renders the nanoparticles insoluble in aqueous solutions. For biological applications nanoparticles must be water soluble. Here we demonstrate the phase transfer of our nanoparticles with the biocompatible copolymer Pluronic F127. Transmission electron microscopy, Fourier transform infrared spectroscopy and dynamic light scattering indicate that the nanoparticles are coated discretely. Magnetic measurements show that the nanoparticles remain superparamagnetic with saturation magnetization ∼96% of the maximum theoretical value.     

Simultaneous best approximation by three polynomials

Let [a, b] be any interval and let p₀, p₁, p_k be any three polynomials of degrees 0, 1, k, respectively, where k 2. A set of necessary and sufficient conditions for the existence of an f in C[a, b] such that p_i is the best approximation to f from the space of all polynomials of degree less than or equal to i, for all i = 0, 1, k, is given.     

A finite difference approach to the equations of age-dependent population dynamics

We establish the convergence of the finite difference scheme for the nonlinear equations of population dynamics proposed by Guertin and MacCamy. The applicability of the discrete equations to establish qualitative properties of the solution to the continuous problem is also illustrated.     

Chvátal closures for mixed integer programming problems

Chvátal introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality. This viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems. The basic ingredient in these cutting-plane proofs is that for a polyhedronP and integral vectorw, if max(wx|x P, wx integer} =t, thenwx t is valid for all integral vectors inP. We consider the variant of this step where the requirement thatwx be integer may be replaced by the requirement that be integer for some other integral vector . The cutting-plane proofs thus obtained may be seen either as an abstraction of Gomory's mixed integer cutting-plane technique or as a proof version of a simple class of the disjunctive cutting planes studied by Balas and Jeroslow. Our main result is that for a given polyhedronP, the set of vectors that satisfy every cutting plane forP with respect to a specified subset of integer variables is again a polyhedron. This allows us to obtain a finite recursive procedure for generating the mixed integer hull of a polyhedron, analogous to the process of repeatedly taking Chvátal closures in the integer programming case. These results are illustrated with a number of examples from combinatorial optimization. Our work can be seen as a continuation of that of Nemhauser and Wolsey on mixed integer cutting planes.Supported by Sonderforschungsbereich 303 (DFG) and by NSF Grant Number ECS-8611841.Supported by NSF Grant Number ECS-8418392 and Sonderforschungsbereich 303 (DFG), Institut für Ökonometrie und Operations Research, Universität Bonn, FR Germany.     

Synthesis and characterization of liquid‐crystalline polyphosphonates containing disubstituted ferrocene esters as mesogens

A series of ferrocene‐containing liquid‐crystalline polyphosphonates with an even number of methylene groups are reported. All the polymers gave birefringent melts. The mesophase was identified as transparent with an increase in the spacer. The effects of pendant substitution and the spacer were studied with thermogravimetric analysis and differential scanning calorimetry. The effects of the phosphonate group in the spacer and the ferrocene ester group in the mesogen were examined. The presence of a steplike mesogenic structure and a pendant phenyl group in the spacer led to reductions in the glass‐transition and melting temperatures. The ferrocene moiety in the mesogen might be one of the reasons for the increased thermal stability and decreased liquid crystallinity. An energy‐minimized structure for the mesogenic and spacer segments was created with computer‐modeling programs, and it suggested the reason for the reductions in the glass‐transition and melting temperatures. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2256–2263, 2002     

A semi-discrete convergent scheme for a quasilinear hyperbolic equation

We establish here the convergence (thereby proving the existence) of a semi-discrete scheme for the quasilinear hyperbolic equation where x ∈ Rⁿ, t ∈ [0,T], and ? ∈ L^∞ (Rⁿ). It is well known that the above problem does not necessarily have global classical solutions and the usual concepts of weak solution. do not lead to a unique solution The existence of a unique solution to the above problem in a suitable sense was established in [3], where a parabolic problem obtained by introducing the term ??Δu was studied and then the behavior as ? → 0 was discussed. A difference scheme approach to a problem of the above type where ?_i does not depend on x and t and Ψ does not depend on u was also studied in [2]. The aim of this paper is to present a proof for the case when ? depends on x, Ψ depends on u, and the technical complications in this case are nontrivial. The discussions in this paper my be considered as continuation of the ideas in the above papers.     

DSC study on the effect of isocyanates and catalysts on the HTPB cure reaction

The urethane forming cure reactions of hydroxyl terminated polybutadiene (HTPB) binder with three different isocyanate curatives, viz., toluene diisocyanate (TDI), isophorone diisocyanate (IPDI) and 4,4-methylene bis(cyclohexyl isocyanate) (MCHI), were investigated by differential scanning calorimetry (DSC). The effect of two cure catalysts, viz., dibutyl tin dilaurate (DBTDL) and ferrric tris-acetylacetonate (FeAA) on the cure reactions was also studied. Cure kinetics was evaluated using the multiple heating rate Ozawa method. The reactivities of the three isocyanates and catalytic efficiencies were compared based on the DSC reaction temperatures, activation energies and rate constants. Viscosity build-up in these systems at isothermal temperature was also studied and compared with the results from DSC.     

Bis(trimethylphosphine)silver(I) hexafluorophosphate

In the title two‐coordinate silver compound, [Ag(C₃­H₉­P)₂]­PF₆, the cation has crystallographically imposed mirror symmetry, and approximates very closely to m (D_3d) symmetry with fully staggered methyl groups in the solid state. The Ag atom has a nearly linear coordination geometry, with a P—Ag—P angle of 178.70 (4)°. The Ag—P bond lengths are 2.3746 (12) and 2.3783 (12) Å, which are ­significantly longer than the Au—P bond length of 2.304 (1) Å in the analogous two‐coordinate gold cation. The lack of intra­molecular steric effects within the present cations containing tri­methyl­phosphine (cone angle 118°), compared with those in known cations containing trimesityl­phosphine (cone angle 212°), provides a better comparison of M—P distances and thus more conclusive evidence that Au really is smaller than Ag.     

Spectral Characteristics of Bicalutamide Drug in Different Solvents and β-Cyclodextrin

Absorption and fluorescence spectra of bicalutamide (BCA) in different solvents and aqueous β-cyclodextrin (β-CD) solutions are reported. The solid inclusion complex of BCA with β-CD is prepared and investigated by FT-IR, ¹H NMR, differential scanning colorimetry (DSC) and scanning electron microscopy (SEM). The Stokes shift of BCA is correlated with various solvent polarity scales like E _T(30), BK and f(D,n). β-CD studies show that (i) the absorption and emission maxima of BCA are shifted to red, (ii) the absorbance is slightly decreased whereas emission intensity is increased largely with an increasing β-CD concentration, (iii) BCA forms 1:1 inclusion complex with β-CD and (iv) intramolecular charge transfer (ICT) emission is present in the excited state.     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....